The Throne Room definitely loses track of the Feast before the second play. The TR/Mining Village situation is the same, and there it's clear that if the MV is trashed on the first play, then the TR loses track of it. Even though TR has lost track of the Feast, it can still play it, because the only thing you can't do to a lost card is move it.
Ok, so by "loses track of" you actually mean a technical definition that boils down to "can't move it". Fine.
So, your theory is that the Throne Room can't move the Feast, but can and does read the text on the physical card in the trash and follow it as far as is possible (i.e. giving you a card).
My theory is that the Throne Room reads the text on the card and then executes those instructions twice. Note that in my psuedocode, the CardPlayingHelperObject retains a reference to the original PhysicalCard, which is how it knows to physically move the card from your hand to the play area, and then from the play area to the trash the first time the Throne Room plays the card.
The difference between your reading and mine comes with the fact that, from the way most people understand the trash, a trashed card is "gone". You don't read the text of a card in the trash unless you played a special card that actually looks at the cards in the trash pile. To represent the normal understanding of what happens to a card when it goes into the trash in our programming code, you could say that the value of PhysicalCard y is now NULL. The way my theory works, this doesn't even matter. ThroneRoom will do the set of instructions twice whether the physical card no longer exists, whether it is truly lost so that ThroneRoom can't even read it, whether it is "psudeo-lost" under the technical definition that really means only "can't move it", or whether it is in a known location such as the play area or in your hand.
My theory is consistent with Donald X's original ruling on how Feast works, it is consistent with Donald X's new ruling on how Band of Misfits works, it is consistent with the TR/Mining Village ruling. The only thing it is not consistent with is your intuition that throne room must read the physical card twice as part of the definition of playing it. What's crazy is that with Band of Misfits, you don't even read the physical text of the card at all, if anything you are reading the physical text of the card it is masquerading as.
Here's another consequence of your theory that I just thought of: suppose you Throne Room a Band of Misfits and choose Ambassador as the card to emulate. Suppose there is one Ambassador left in the supply. Further suppose you reveal an Ambassador from your hand and choose to return no copies of the ambassador to the supply, causing your opponent to pick up the last Ambassador.
According to your theory that Throne Room re-evaluates the card when playing it a second time, wouldn't it make sense that the Throne Room actually picks up the card from the play area (since according to you it has not yet 'lost track of it' which just means 'it can move it') removing it from play temporarily even in the normal case that doesn't involve the trash, in preparation for playing it again?
If this is the case, then Band of Misfits is a Band of Misfits again once it is back in your hand ready to be played again, but this time you can't legally pick Ambassador since there are no copies of it in the supply. I think most people would clearly play this: I play a Throne Room and pick Band of Misfits. I'm playing my Band of Misfits as an Ambassador, so I do the Ambassador action twice. Also, this is how Donald X. says it should be played.